Search

Nonlinear expressions are often approximated by piecewise affine (PWA) functions to simplify analysis or reduce computational costs. To reduce computational complexity, multivariate functions can be represented as compositions of functions with one or two inputs, which can be approximated individually. This paper provides efficient methods to generate PWA approximations of nonlinear functions via functional decomposition. The key contributions focus on intelligent placement of breakpoints for PWA approximations without requiring optimization, and on bounding the error of PWA compositions as a function of the error tolerance for each component of that composition. The proposed methods are used to systematically construct a PWA approximation for a complicated function, either to within a desired error tolerance or to a given level of complexity.

This paper proposes a method for set-valued state estimation of nonlinear, discrete-time systems. This is achieved by combining graphs of functions representing system dynamics and measurements with the hybrid zonotope set representation that can efficiently represent nonconvex and disjoint sets. Tight over-approximations of complex nonlinear functions are efficiently produced by leveraging special ordered sets and neural networks, which enable computation of set-valued state estimates that grow linearly in memory complexity with time. A numerical example demonstrates significant reduction of conservatism in the set-valued state estimates using the proposed method as compared to an idealized convex approach.

This paper proposes methods for reachability analysis of nonlinear systems in both open loop and closed loop with advanced controllers. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition, and special ordered set approximations to enable linear growth in reachable set memory complexity with time and linear scaling in computational complexity with the system dimension. Facilitating this combination are new identities for constructing nonconvex sets that contain nonlinear functions and for efficiently converting a collection of polytopes from vertex representation to hybrid zonotope representation. Benchmark numerical examples from the literature demonstrate the proposed methods and provide comparison to state-of-the-art techniques.

Enceladus is believed to have a saltwater global ocean with a mean depth of at least 30~km, heated from below at the ocean-core interface and cooled at the top, where the ocean loses heat to the icy lithosphere above. This scenario suggests an important role for vertical convection to influence the interior properties and circulation of Enceladus' ocean. Additionally, the ice shell that encompasses the ocean has dramatic meridional thickness variations that, in steady state, must be sustained against processes acting to remove these ice thickness anomalies. One mechanism that would maintain variations in the ice shell thickness involves spatially-separated regions of freezing and melting at the ocean-ice interface. Here, we use an idealized, dynamical ocean model forced by an observationally-guided density forcing at the ocean-ice interface to argue that Enceladus' interior ocean should support a meridional overturning circulation. This circulation establishes an interior density structure that is more complex than in studies that have focused only on convection, including a shallow freshwater lens in the polar regions. Spatially-separated sites of ice formation and melt enable Enceladus to sustain a significant vertical and horizontal stratification, which impacts interior heat transport, and is critical for understanding the relationship between a global ocean and the planetary energy budget. The presence of low salinity layers near the polar ocean-ice interface also influences whether samples measured from the plumes are representative of the global ocean.

The Beaufort Gyre freshwater content has increased since the 1990s, potentially stabilizing in recent years. The mechanisms proposed to explain the stabilization involve either mesoscale eddy activity that opposes Ekman pumping or the reduction of Ekman pumping due to reduced sea ice?ocean surface stress. However, the relative importance of these mechanisms is unclear. Here, we present observational estimates of the Beaufort Gyre mechanical energy budget and show that energy dissipation and freshwater content stabilization by eddies increased in the late-2000s. The loss of sea ice and acceleration of ocean currents after 2007 resulted in enhanced mechanical energy input but without corresponding increases in potential energy storage. To balance the energy surplus, eddy dissipation and its role in gyre stabilization must have increased after 2007. Our results imply that declining Arctic sea ice will lead to an increasingly energetic Beaufort Gyre with eddies playing a greater role in its stabilization.

UNKNOWN

UNKNOWN

UNKNOWN

This work describes a planning architecture for a heterogeneous fleet of marine assets as well as a method for detecting and tracking ocean fronts using multiple autonomous underwater vehicles. Multiple vehicles — equally-spaced along the expected frontal boundary — complete near parallel transects orthogonal to the front. Lateral gradients are used to determine the location of the front crossing from each individual vehicle transect by detecting a change in the observed water property. Adaptive control of the vehicles ensure they remain perpendicular to the estimated frontal boundary as it evolves over time. This method was demonstrated in several experiment periods totaling weeks, in and around Monterey Bay, California in May and June of 2017. We discuss the challenges associated with the implementation of the planning system. We show the capability of this method for repeated sampling across a dynamic two-dimensional ocean front using a fleet of three types of platforms: short-range Iver AUVs, Tethys-Class Long-Range AUVs, and Seagliders. This method extends to tracking gradients of different properties using a variety of vehicles.

This work describes a method for detecting and tracking ocean fronts using multiple autonomous underwater vehicles. Multiple vehicles — equally-spaced along the expected frontal boundary — complete near parallel transects orthogonal to the front. Lateral gradients are used to determine the location of the front crossing from each individual vehicle transect by detecting a change in the observed water property. Adaptive control of the vehicles ensure they remain perpendicular to the estimated front boundary as it evolves over time. This method was demonstrated in and around Monterey Bay, California in May of 2017. We compare the front detection method to previously used methods. We introduce a metric in order to evaluate the adaptive control techniques presented. We show the capability of this method for repeated sampling across a dynamic two-dimensional ocean front using short-range Iver AUVs. This method extends to tracking gradients of different properties using a variety of vehicles.

UNKNOWN

UNKNOWN